Dynamics of Air-Fluidized Granular System Measured by the Modulated Gradient Spin-echo

Abstract

The power spectrum of displacement fluctuation of beads in the air-fluidized granular system is measured by a novel NMR technique of modulated gradient spin-echo. The results of measurement together with the related spectrum of the velocity fluctuation autocorrelation function fit well to an empiric formula based on to the model of bead caging between nearest neighbours; the cage breaks up after a few collisions \cite{Menon1}. The fit yields the characteristic collision time, the size of bead caging and the diffusion-like constant for different degrees of system fluidization. The resulting mean squared displacement increases proportionally to the second power of time in the short-time ballistic regime and increases linearly with time in the long-time diffusion regime as already confirmed by other experiments and simulations.